ANALYSIS ON THE SPINNING FORCES IN FLEXIBLE SPINNING OF CONES

CHINESE JOURNAL OF MECHANICAL ENGINEERING●376.Vol.16, No.4, 2003ANALYSIS ON THE SPINNING FORCESXia QinxiangDepartment of Mechanical Engineering,IN FLEXIBLE SPINNING OF CONESSouth China University of Technology.Guangzhou 510640, ChinaTBI24 ASusumu ShimaDeparment of Mechanical Engineening.Abstract:. Flexible spinning is a new type of spinning process where sin-forming is performedwithout using a mandrel. Combining shearing and rlling processes, the calculation formulas of theKyoto Universiy,spinning fores in flexible spinning of cones is presented. The effects of the main processing parame-Kyoto 606-8501, Japanters, such as gripping force G applied to the blank by the inner rllr, the feed rate of rllers and theroundness radius of outer roller Fo on the spinning forces ate analyzod experimentally and theoreti-cally.Key words: Spinning force Flexibility Spin-forming Cone(2) In the rlling deformnation region. the plastic deformation0 INTRODUCTIONis caused by both the outer and inner rollers. It is assumed that thecontact stress is equal to each other on the two sides of the blank[3]With the development of industrial technology and the im- because of the small contact area in this region.provement of the living standards, the variety of product is neces-(3) In the pure shearing deformation rgion, the deformationsary for enterprises to win the market competition. In recent years, is caused only by the outer roller. It is assumed that there is onlythe incremental forming process with large. fexibili, which is the pure shearing deformation along the axial direction.suitable for the. various small batch productions, has been inten- 1.1 Calculation of contact areas between rollers aod blaoksively studiede. Conventional spinning proccss is a typical in-The contact and projective areas between the blank and roll-cremental forming process, where only the mandrel is designeders are shown in Fig.2. The contact area S between the inner rollerfor the produer, therefore it belongs to a kind of semi mandand the blank iis related to e, the depth of the inner rller, pressingforming processcs. In order to improve the operating efficiency into the blank (see Fig.1 and Fig 2b).and reduce the cost of such product more effectively, SusumaShima et a|4] have developed the new spinning process, flexiblespinning, where spinning is perfored by a pair of rollers withoutSousing a mandrel. Forming cones by flexible spinning was carriedout as follows (see Fig.l)( Biank1 Roller pathK大Rhearin"Rolling nrea (1)Outer rollerfFait一Inner roller(a(b)Fig.1 Schematic drawing of flexible sinning(1) Rotate a circular sheet metal blank as in the conventionalspinning.(2) The rotating blank is gripped by a pair of rllrs.(3) The rllers gripping the blank move along the same paths the shape of part, so that a required axis- symmetric shape canbe formed.aS1 FORMULAS OF SPINNING FORCESarecomg，十r.(1-sina)The following assumptions are adopted in this paper.(c)(1) The flexible spinning proccss is treated as a combina-Fig.2 Contact and projective areas between the blank and rllerstion of shearing and rolling processes. The total deformationzone is divided into two regions by line oP, as shown in Fig.1,Because S is small, the shapc of the blank near the contactwhere point 0 is the center of the roundness of the outer rllre area can be asumed as a plane, hencepoint P is the contact edge point between the inner roller andS.≈0.5ab1)中国煤化工2)3)[HCNMHGa| piecivcaeReeived January I1, 2002; received in revised form March 21. 2003; acceptedvhere "i讷2; u wH en4 ugental projofSJune 1s, 2003CHINESE JOURNAL OF MECHANICAL ENGINEERING●377.a,b.- Maximum axial and tanganial contat lenghs be- shearing region aretween the inner rller and blankSr2=Sor - Sur(10)f一Feed rate of the rllrs(1I)a:=√e(2r-e)Sor=Sop- Sou(12)b;≈√e(2R,-e).2 Calculation of spinning forcesThree components Fin Fsin Fsio of spinning force P of the一Roundness radiusinner rller are (as shown in Fig.1a)R:一Radius of the inner rollerFsy=Fx(13)According to the platic principle, when contact stres σ be.tween the inner roller and blank equals to K(2+r), plastic defor-Fu =1.483σ,eb,(14)mation occurs, where K is the yield stress of the pure shearingFsio = 1.4830o,ef(15)deformation!. Using Mises yield condition, K=0.577σ,，so in theIn the rlling region of the outer rlle, according to the pre-rolling region of the inner rlle, σ:=2.9660, Sn=F/o. where, 0vious assumption, the contact stess σol between the outer rolleris yield stess of the material, G is gripping force applied to theand blank equals to a. The radial, axial and tangential compo-blank by the inner roller. Hence, contact area S between the blanknents Fsorl, Fsax1 and Fsoa of spinning force F。1 of the outer rollerand inner roller is obtained.Total contact area S。between the outer rller and blank isin the rolling region areshown in Fig.2c. Radial, axial and tangential projctive areas Sor,Forn=Srσ,(16)Sa,Suq ofS areRa=Sσ,(17)Sow≈0.5r.R cosax(4Poon =SoaoS。。0.5r。R,(l1-sina)(5In the pure shearing region, the deformation work则of theSa≈0.5fr(1- sina)(6material iswhere r。一 -Roundness radius of the outer rollerW=1.154π Rnfoσ, cos(a + Qa)R一-Radial distance of the initial point of the deforma-tion zoneSa = arcsi2θ一Tangential included angle of the deformation zone)x- - Half- cone angle of the workpicceR=0.5d。+ zsina +r。cosaWork Wz done by the tangential component Fmo2 of sinningforce Fo2 of the outer roller isb2w2 = 2π RnFo02θ= accswhere n一-Rotation speed of the blankW=Wthusn1=。-f cosaFour =0.577σ,fto cos(a + OQ)b= 2(R。-0↓7 - (ncosB) - rsinβ|+a'Hence, radial and axial components Fornr, Fsa2 of Fo2 in thepure shearing region ared,--Diamcter of the workpiece bottom(20)z一Coordinate value of the ending point of the def-Fsau2 =SarOw(21)ormation zone on the slant wall of the workpiecewhere σov一Average contact stress in the pure shearing regionRadius of the outer rollerbetween the outer roller and blankInsaling angle of the outer rollereFxz_ 1.154s.ft. cos(ax + Da)Radial, axial and tangential projective areas Sort，Sal, Som offr(1-sina)-La。contact arca Sou between the outer toller and blank in the rollingIn the actual spinning process, the contact stress is small inregion, as shown in Fig.2c, areSor]≈0.5sa。b。(7the initial positon of the deformation (point M in Fig.l) and islarge near the rolling region (point N in Fig.1). Thus, Fgor in .Soel≈0.5hb。Son≈0.5La。(9Eq.(20) is less than the actual one, and Fxar2 in Eq.(21) is largerthan the actual one, Using two modification cofficients C, C1, C: and C, meet the condition that Fso2 keeps con-tact lengths between the outer rller and stant in the shearing region, that isblank in the rolling regiona。=rsinφC,=-S2+S2-CS2(22)φ= arctanHence, the total radial, axial and tangential spinning forces(r+i+e)Fovr, Foar, Fso of the outer roller are1=tgsinaFo =Fan +C.Fxr(23)o,1一-Thickness of the blank and workpieceFsa =Fmn+C.Fra2(24)h=h=n-Vo2-a2Foa =Frol +F.ow2.(25)b。=R.sinpLetcos(a + Da)φ≈arctanR+R+1-VR-B )中国煤化工efa.0- sina) .MYHC NM H G.,6(2s.。-a.02)] (26)r。cosa(r。cosa- f)F, = 0577,[2.57hb。+ AC.l(2S& - hb.,)(27)Radial, axial and tangential projecive areas So2 Su2, Soe20fE,=0577s,[2.57La。+ A16(2S。- La.)]the contact area Sa2 between the outer roller and blank in the pure●378.Xia Qinxiang, et上Analysis on the sinning forces in flexible spnning of coneswith increasing r。because of the smooth outer roller. The spin-2 COMPARISON OF EXPERIMENTAL ANDning forces arc not related to the inner roller and ro(see Eqs.(13)CALCULATION RESULTSto(15)), so Fur and Fu change slightly with increasing r。400-2.1 Experimental conditionThe materials used for the circular blank was commercially300-pure aluminum (O statel); diameter Do 200 mm; thickness to=10nm. The rotation speed of the blank n=300 r/min. Let the modi-fication cefficient C=0.8. The relationship between half-coneangle a of the workpiece and installing angle β of the outer rollerisa= =β=45', so that the moving direction of the rollers is parallelto the common tangent at the contact area between the rollers andthe workpiece'"l. The diameter of the inner roller D=S0 mm; and025°18250315the roundness radius of the inner roller r;=6 mm. The diameter ofGriping force F/Nthe outer roller D。=80 mm; and the roundness radii of the outerFig.4 Comparison of experimental and calculatio tresultsroller ro were 4 mm, 5 mm and 6 mm respectively. The range offor dferent F (ro= 6 mm,f 0.3 mn/t)feed rate of the roller per revolution f was from 0.08 to 0.4 mm/t.Gripping forces Fg were0N, 125 N, 188 N, 250 N and 315 N300~Fu-Trespectively. The experiment was carried out on RH-L3A Proc-Fi-Tessing Robot made by Nihon Mitsubishi Company,2.2 Experiment results。200- F-_基--。Both the calculation and experiment ilustrate that the tan-gential components of the spinning forces of the outer and innerrollers were small, so they were not considered in this paper. Fig.3品100-shows the comparison of the spinning forces between the experi-mental and calculation results for different f, where T and C Teferto the experimental and calculation spinning forces, respectively.It shows that the calculation results conform well to the experi-Roundness radius ro/mmmental ones. Fig.3 also shows that both Fsor and Fax increase withFig.5 Comparison of experimental and calculation resultsincreasing f, and there are no change for Fswr and Fsua when Fgfor difent r.(-0.34 mm, F;=188 N)keeps constant. Larger J, the more material volume deformed perunit time, hence an increase in the deformation power, therefore3 CONCLUSIONSan increase in the spinning force of the outer roller. On the otherhand, Fsir depends on Fg only (see Eq(13)); and Fue depends onThe spinning forces of the flexible spinning of cones arethe property of the material, the radius of the inner roller r, and theanalyzed experimentally and theoretically. The study demon-dcepth of the inner roller pressing into blank e, hence there are nostrates the main findings as follows.change for Fsw and Fsiu when Fg keeps constant,(1) The formulas of the spinning forces can be obtained bydividing the deformation zone into shearing and rolling regions inflexible spinning.Fir-T(2) The gripping force Fg applied to the blank, the feed rate .of the rollersf and the roundness radius of the outer roller o, have20-ogreat influence on the spinning force in flexible spinning of cones.(3) The calculation results conform well to experimental onesfor many different working conditions, error is less than土20%，100-References- ----Fa-C0.1 0.2 0.31 島進，小寺秀俊,村上浩隆.午心厂几x比s T几又比二二夕加工法口開凳.塑性上加工，1997, 38(9): 40- 44Feed rate f/(mm2松原茂夫. 数值控制逐次成形法，塑性上加工I, 194, 35(1) 1258-1263Fig.3 Comparison of cxperimental and calculation resuts王成和、值控制建次成地法，for dfferentf(r=S mm, Fg-188 N)3王成和刘克璋旋压技术.北京:机械工业出版社, 19864汪大年，金属塑性成形原理.北京:机械工业出版社, 1982Fig.4 shows the comparison of the spinning forces betweenBlographicsl notes: Xia Qinxiang is助n associate professor in Department ofthe experimental and calculation results for different Fg It showsMechanical Engineering. South China University of Technology, China, Shethat all the components of the spinning forces increase with in-recceived her MS degree from College of Material Science and Enginering ofcreasing F. This is due to the fact that when Fg inncreases the Northwestem Polytecbnical Universit, Ching, in 1988 Her restarch interestsdepth of the inner roller pressing into blank e incrcases.inelude plastic forming theory, tchnology and machine, FEA, CAD/CAM, etc.Fig.s shows the comparison of the sinning forces between Tel: -82038621818 Emai: mxicu.d. cnthe experimental and calculation results for different r。It showsthat For increases and Fx decreases a ltte with increasing ro; and Susumu Sima is a professor in Department of Mechanical Engineering, Kyotothe spinning forces of the inner roller change slightly Asr。in- University, Japan. His research subjecs include development of nilligentcreases, the contact area between the outer rller and blank S。metal forming poeses,s plstie defomation of inomogcncous maerals,sincreases, and hence an increase in Fsor (see Fig.2). However, thebebavior of lttice defects during plastic deformation, etc.axial deformation resistance of the deformed material decreasesTel: +81-75-7535229; E-mail: shina@mech.kyoto-u.acjp中国煤化工YHCNMHG